Abstract
The goal of this research is to study the performance of meshless approximations and their integration. Two diffuse shape functions, namely the moving least-squares and local maximum-entropy function, and a linear triangular interpolation are compared using Gaussian integration and the stabilized conforming nodal integration scheme. The shape functions and integration schemes are tested on two elastic problems, an elasto-plastic problem and the inf-sup test. The elastic computation shows a somewhat lower accuracy for the linear triangular interpolation than for the two diffuse functions with the same number of nodes. However, the computational effort for this interpolation is considerably lower. The accuracy of the calculations in elasto-plasticity depends to great extend on the used integration scheme. All shape functions, and even the linear triangular interpolation, perform very well with the nodal integration scheme and locking-free behavior is shown in the inf-sup test.
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Acknowledgments
This research was carried out under project number MC1.07291 in the framework of the Research Program of the Materials innovation institute M2i (http://www.m2i.nl), the former Netherlands Institute for Metals Research.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Quak, W., van den Boogaard, A.H., González, D. et al. A comparative study on the performance of meshless approximations and their integration. Comput Mech 48, 121–137 (2011). https://doi.org/10.1007/s00466-011-0577-6
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DOI: https://doi.org/10.1007/s00466-011-0577-6